Single-Channel Color Image Encryption Using the ... - Semantic Scholar
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JOURNAL OF COMPUTERS, VOL. 8, NO. 11, NOVEMBER 2013
Single-Channel Color Image Encryption Using the Reality-Preserving Fractional Discrete Cosine Transform in YCbCr Space Jianhua Wu, Fangfang Guo Nanchang University/Department of Electronic Information Engineering, Nanchang 330031, China Email: [email protected] (JH Wu), [email protected] (FF Guo)
Nanrun Zhou* Nanchang University/Department of Electronic Information Engineering, Nanchang 330031, China Beijing University of Posts and Telecommunications/Information Security Center, Beijing 100876, China Email: [email protected]
Abstract—A novel single-channel color image encryption algorithm is proposed, which utilizes the reality-preserving fractional discrete cosine transform in YCbCr space. The color image to be encrypted is decomposed into Y, Cb, and Cr components, which are then separately transformed by Discrete Cosine Transform (DCT). The resulting three spectra sequences, obtained by zig-zag scanning the spectra matrices, are truncated and the lower frequency coefficients of the three components are scrambled up into a single matrix of the same size with the original color image. Then the obtained single matrix is encrypted by the fractional discrete cosine transform, which is a kind of encryption with secrecy of pixel value and pixel position simultaneously. The encrypted image is convenient for display, transmission and storage, thanks to the reality-preserving property of the fractional discrete cosine transform. Additionally, the proposed algorithm enlarges the key space by employing the generating sequence as an extra key in addition to the fractional orders. Simulation results and security analysis demonstrate the proposed algorithm is feasible, effective and secure. The robustness to noise attack is also guaranteed to some extent. Index Terms—single-channel, color image encryption, reality-preserving fractional discrete cosine transform, generating sequence, spectrum truncation
I. INTRODUCTION The reason of the use of color in image processing not only is that color is a powerful descriptor to provide beauty in vision, but also is that humans can discern thousands of color shades and intensities compared with about only two dozen shades of gray. Thus, color images contain more information than gray images do and are widely used in real life. Color image encryption has become a major task for information security since the Manuscript received June 28, 2013; revised August 2, 2013; accepted September 24, 2013. *Corresponding author: [email protected].
© 2013 ACADEMY PUBLISHER doi:10.4304/jcp.8.11.2816-2822
issues about illegal data access on Internet are becoming more and more serious. Past two decades we have witnessed the appearance of various encryption methods for gray images. Amongst, the most famous and widely used one is the double random phase encoding (DRPE) given by Refregier and Javidi[1], which applies two random phase masks arranged separately in the input and the Fourier planes to encrypt the image into a stationary white noise. The two random phase masks are uniformly distributed in the interval [0, 2π] and the second one is taken as the main cipher key. Except the Fourier domain, other different domains such as fractional Fourier transform (FrFT) domain[2-5], Fresnel transform domain[6,7], Hartley transform domain[8,9] and Gyrator transform domain[10-12] are explored for more new encryption methods. However, the decrypted images resulting from optical cryptosystems would lose their color information, which makes these encryption algorithms inappropriate to encrypt color images. In response to this demand, many image encryption schemes especially for color images have been designed, where three components of color image are encrypted using the traditional gray image encryption methods separately[13]. In that case, it renders the cryptosystems sophisticated, since three channels must be involved. To address this problem, various single-channel color image encryption techniques have been put forward successively[14-17]. Zhou et al.[14] proposed a single-channel color image encryption algorithm based on chaotic scrambling and the FrFT in HSI space, the output of the encryption system is not a color image but a gray and a phase matrix. Wu et al.[16] made full use of the complex number mode to realize a single-channel color image encryption in fractional Fourier domain. Although the above discussed encryption methods belong to single-channel, the encrypted images are complex-valued possessing amplitude information as well as phase information, which makes them inconvenient to
JOURNAL OF COMPUTERS, VOL. 8, NO. 11, NOVEMBER 2013
display, transmit and store. In this paper, a novel singlechannel color image algorithm based on the fractional discrete cosine transform (FrDCT)[18], which inherits the reality of the discrete cosine transform (DCT) matrix, is proposed. The original color image is converted into the YCbCr space, where the Y component denotes the brightness, and the Cb and the Cr components respectively denote the color differences of red and blue [16] . Since human eyes are more attuned to brightness and less to color differences, hence the YCbCr color model allows more attention to be paid to the Y component, and less to the others. It is well known that the discrete cosine transform (DCT)[19] has the property of energy concentration, namely, the energy of an image after DCT concentrates towards the top left corner — the low frequency, which human vision is more sensitive to. With the help of spectrum truncation, the low frequency spectra truncated from the corresponding cosine spectra in accordance with the ratio of 2:1:1 are scrambled up into one single matrix and sequentially encrypted by the FrDCT, which has a character of altering the pixel value and the pixel position simultaneously. The resulting cipher-text is a real gray-scale image, which is convenient for display, transmission and storage, and has camouflage property to some extent. Furthermore, generating sequence (GS), which results from the multiplicity of FrDCT matrices’ roots, is introduced as an extra cipher key. Spatiotemporal chaotic map[20] is utilized to generate the random GS. Thus the high sensitiveness to initial values and system parameters inherent in any chaotic system provides high security naturally. Since the fractional orders are not so sensitive compared with the chaotic maps, they can be abandoned or be used merely as auxiliary keys. Simulation results and security analysis verify the effectiveness and feasibility of the algorithm. Robustness to noise attack is also validated. The rest of this paper is organized as follows. Section II describes the theoretical background about the realitypreserving fractional discrete cosine transform. Section III gives the details of the proposed algorithm including the color model, spectrum truncation and the spatiotemporal chaotic map. The procedures of the proposed algorithm are also described in Section III. Simulations and discussions are given in Section IV. Finally, conclusion is drawn in final section followed. II. THEORETICAL BACKGROUND The fractional discrete cosine transform (FrDCT) is a generalization of the DCT. In current literatures, even though several versions of fractional cosine transform have been derived, the FrDCT[18] different from those defined in [21,22] possesses the mathematical properties of reality in addition to linearity, unitarily and additivity. And the reality is of importance for image encryption, which ensures the outputs are real for real inputs. The FrDCT is derived based on the eigendecomposition and eigenvalue substitution of the DCT-II kernel denoted as:
© 2013 ACADEMY PUBLISHER
2817
⎛ ( 2n + 1) k ⎞ 1 ε k cos ⎜ 2π ⎟ 4N ⎠ N ⎝
C=
where n, k = 0,1,… , N − 1
and
(1)
ε0 = 1 , εk = 2
for nonzero k. The eigen-decomposition of an N × N DCI-II matrix C is:
C = UΛU* = ∑ U n e jϕn
(2)
n
where U is a unitary matrix, composed of columns (eigenvectors) u n ,
u*mu n = δ mn , and Λ is the diagonal
matrix with diagonal entries, i.e. eignvalues
λn = e
jϕn
λn
,
with 0 < ϕ n
JOURNAL OF COMPUTERS, VOL. 8, NO. 11, NOVEMBER 2013
Single-Channel Color Image Encryption Using the Reality-Preserving Fractional Discrete Cosine Transform in YCbCr Space Jianhua Wu, Fangfang Guo Nanchang University/Department of Electronic Information Engineering, Nanchang 330031, China Email: [email protected] (JH Wu), [email protected] (FF Guo)
Nanrun Zhou* Nanchang University/Department of Electronic Information Engineering, Nanchang 330031, China Beijing University of Posts and Telecommunications/Information Security Center, Beijing 100876, China Email: [email protected]
Abstract—A novel single-channel color image encryption algorithm is proposed, which utilizes the reality-preserving fractional discrete cosine transform in YCbCr space. The color image to be encrypted is decomposed into Y, Cb, and Cr components, which are then separately transformed by Discrete Cosine Transform (DCT). The resulting three spectra sequences, obtained by zig-zag scanning the spectra matrices, are truncated and the lower frequency coefficients of the three components are scrambled up into a single matrix of the same size with the original color image. Then the obtained single matrix is encrypted by the fractional discrete cosine transform, which is a kind of encryption with secrecy of pixel value and pixel position simultaneously. The encrypted image is convenient for display, transmission and storage, thanks to the reality-preserving property of the fractional discrete cosine transform. Additionally, the proposed algorithm enlarges the key space by employing the generating sequence as an extra key in addition to the fractional orders. Simulation results and security analysis demonstrate the proposed algorithm is feasible, effective and secure. The robustness to noise attack is also guaranteed to some extent. Index Terms—single-channel, color image encryption, reality-preserving fractional discrete cosine transform, generating sequence, spectrum truncation
I. INTRODUCTION The reason of the use of color in image processing not only is that color is a powerful descriptor to provide beauty in vision, but also is that humans can discern thousands of color shades and intensities compared with about only two dozen shades of gray. Thus, color images contain more information than gray images do and are widely used in real life. Color image encryption has become a major task for information security since the Manuscript received June 28, 2013; revised August 2, 2013; accepted September 24, 2013. *Corresponding author: [email protected].
© 2013 ACADEMY PUBLISHER doi:10.4304/jcp.8.11.2816-2822
issues about illegal data access on Internet are becoming more and more serious. Past two decades we have witnessed the appearance of various encryption methods for gray images. Amongst, the most famous and widely used one is the double random phase encoding (DRPE) given by Refregier and Javidi[1], which applies two random phase masks arranged separately in the input and the Fourier planes to encrypt the image into a stationary white noise. The two random phase masks are uniformly distributed in the interval [0, 2π] and the second one is taken as the main cipher key. Except the Fourier domain, other different domains such as fractional Fourier transform (FrFT) domain[2-5], Fresnel transform domain[6,7], Hartley transform domain[8,9] and Gyrator transform domain[10-12] are explored for more new encryption methods. However, the decrypted images resulting from optical cryptosystems would lose their color information, which makes these encryption algorithms inappropriate to encrypt color images. In response to this demand, many image encryption schemes especially for color images have been designed, where three components of color image are encrypted using the traditional gray image encryption methods separately[13]. In that case, it renders the cryptosystems sophisticated, since three channels must be involved. To address this problem, various single-channel color image encryption techniques have been put forward successively[14-17]. Zhou et al.[14] proposed a single-channel color image encryption algorithm based on chaotic scrambling and the FrFT in HSI space, the output of the encryption system is not a color image but a gray and a phase matrix. Wu et al.[16] made full use of the complex number mode to realize a single-channel color image encryption in fractional Fourier domain. Although the above discussed encryption methods belong to single-channel, the encrypted images are complex-valued possessing amplitude information as well as phase information, which makes them inconvenient to
JOURNAL OF COMPUTERS, VOL. 8, NO. 11, NOVEMBER 2013
display, transmit and store. In this paper, a novel singlechannel color image algorithm based on the fractional discrete cosine transform (FrDCT)[18], which inherits the reality of the discrete cosine transform (DCT) matrix, is proposed. The original color image is converted into the YCbCr space, where the Y component denotes the brightness, and the Cb and the Cr components respectively denote the color differences of red and blue [16] . Since human eyes are more attuned to brightness and less to color differences, hence the YCbCr color model allows more attention to be paid to the Y component, and less to the others. It is well known that the discrete cosine transform (DCT)[19] has the property of energy concentration, namely, the energy of an image after DCT concentrates towards the top left corner — the low frequency, which human vision is more sensitive to. With the help of spectrum truncation, the low frequency spectra truncated from the corresponding cosine spectra in accordance with the ratio of 2:1:1 are scrambled up into one single matrix and sequentially encrypted by the FrDCT, which has a character of altering the pixel value and the pixel position simultaneously. The resulting cipher-text is a real gray-scale image, which is convenient for display, transmission and storage, and has camouflage property to some extent. Furthermore, generating sequence (GS), which results from the multiplicity of FrDCT matrices’ roots, is introduced as an extra cipher key. Spatiotemporal chaotic map[20] is utilized to generate the random GS. Thus the high sensitiveness to initial values and system parameters inherent in any chaotic system provides high security naturally. Since the fractional orders are not so sensitive compared with the chaotic maps, they can be abandoned or be used merely as auxiliary keys. Simulation results and security analysis verify the effectiveness and feasibility of the algorithm. Robustness to noise attack is also validated. The rest of this paper is organized as follows. Section II describes the theoretical background about the realitypreserving fractional discrete cosine transform. Section III gives the details of the proposed algorithm including the color model, spectrum truncation and the spatiotemporal chaotic map. The procedures of the proposed algorithm are also described in Section III. Simulations and discussions are given in Section IV. Finally, conclusion is drawn in final section followed. II. THEORETICAL BACKGROUND The fractional discrete cosine transform (FrDCT) is a generalization of the DCT. In current literatures, even though several versions of fractional cosine transform have been derived, the FrDCT[18] different from those defined in [21,22] possesses the mathematical properties of reality in addition to linearity, unitarily and additivity. And the reality is of importance for image encryption, which ensures the outputs are real for real inputs. The FrDCT is derived based on the eigendecomposition and eigenvalue substitution of the DCT-II kernel denoted as:
© 2013 ACADEMY PUBLISHER
2817
⎛ ( 2n + 1) k ⎞ 1 ε k cos ⎜ 2π ⎟ 4N ⎠ N ⎝
C=
where n, k = 0,1,… , N − 1
and
(1)
ε0 = 1 , εk = 2
for nonzero k. The eigen-decomposition of an N × N DCI-II matrix C is:
C = UΛU* = ∑ U n e jϕn
(2)
n
where U is a unitary matrix, composed of columns (eigenvectors) u n ,
u*mu n = δ mn , and Λ is the diagonal
matrix with diagonal entries, i.e. eignvalues
λn = e
jϕn
λn
,
with 0 < ϕ n
